You have created a false reality, and then cried foul when real life didn't play ball.
Wouldn't a reality where land is only held by those using it and you can buy land for a quarter be better? I don't even mean to be funny or anything but that seems like a much better situation that our current one.
Arguably there are two big problems with the market for land/housing, and landlords aren't one o them:
#1 Increases the value of land due to neighbourhood effects accrue to the owner when they do little to deserve it (you can tackle this with land-value taxes).
#2 Various planning controls inhibit the market's ability to respond to high accomodation prices with the construction of more accomodation, keeping rents at a higher level than they would otherwise be without this government intervention.
Buildings should be 'permitted' to be built on land, and people can own the land insomuch as they pay land value taxes for the utilization of the land. If it's a primary purpose and they don't get income from it, then the tax would be nil, if it's a second home they'd get 90% off as they're still a 'small fry', maybe 3-10 homes is 50% of full tax, and 10+ is the full tax.
LVT can then be funneled into housing programs, housing assistance funds, or straight up basic income.
Land value tax is the tax of the value the owner gets from the land, so if you're airbnb'ing you'd pay more if you make 10k per month in airbnb, then if you're renting long-term for 2k/month. If you still have a mortgage, you could maybe have some sort of deduction - but again that's only if you're owning 3 or less homes, anyone leveraging credit for 10+ homes should be able to afford mortgage out of their normal cash-flows, or they're over-levereged and need to dump a property or two.
Seems like a perverse incentive to me.